University of TabrizComputational Methods for Differential Equations2345-39828420201101Optimal homotopy asymptotic and multistage optimal homotopy asymptotic methods for Abel Volterra integral equation of the second kind770780991410.22034/cmde.2020.26806.1349ENJafarBiazarDepartment of Mathematics, Faculty of Sciences, University of Guilan, P.C. 41938 Rasht, Iran0000-0001-8026-2999RoyaMontazeriDepartment of Mathematics, Payame Noor University,
P. O. Box 19395-3697, Tehran, Iran.Journal Article20180415In this paper, optimal homotopy asymptotic method (OHAM) and multistage optimal homotopy asymptotic (MOHAM) method are applied to find an approximate solution to Abelâ€™s integral equation, that is in fact a weakly singular Volterra integral equation. To illustrate these approaches one example is presented. The results confirm the efficiency and ability of these methods to such equations. The results will be compared with the exact solution to find out that which method of these two is more accurate.https://cmde.tabrizu.ac.ir/article_9914_8b268d400c57e3033b79e2ecbafb48c7.pdf